A WG sapphire resonator consists of a ring or disk of sapphire inside a metallic cylindrical casing for electromagnetic shielding of and confining resonating rf fields to the sapphire element. These resonators effectively eliminate rf conduction losses and thus make possible oscillators that are only limited by performance of the sapphire itself. The sapphire is typically oriented with its crystal c-axis along the axis of the cylindrical casing in order to achieve cylindrical symmetry for the excited electromagnetic resonance modes.
WG electromagnetic modes can be divided into families depending on their field configuration, and further characterized by the number n of full waves around the perimeter of the sapphire ring or disk. The modes are doubly degenerate, with azimuthal phase of the two submodes differing by 90.degree.. Modes typically used are the WGH.sub.n11 family for ring resonators and the WGE.sub.n11 family for flat disk resonators, where n.gtoreq.5. WG denotes Whispering Gallery and H.sub.n11 denotes electric field loops formed in the annular body of a wheel or ring, and E.sub.n11 denotes electric field loops formed in the planar body of a sapphire disk.
With very high microwave quality factors (Q's) at easily reached cryogenic temperatures, the sapphire resonators already make possible excellent phase noise performance. In principle, the high Q values also make possible high frequency stability, but only if the resonator itself were stable. Temperature fluctuations in the sapphire cause unwanted frequency fluctuations in the resonator. If these frequency variations could be cancelled or compensated, high stability could be achieved.
Q of the WG sapphire resonator increases rapidly as the temperature is cooled, from approximately Q=300,000 at 300.degree. K (room temperature) to 30 million at 77.degree. K (for X-band frequencies.apprxeq.8 GHz). This compares to Q values of 1 to 2 million for the best available crystal quartz oscillators, and 10,000 to 20,000 for metallic microwave cavities. Consequently, when coupled with low noise microwave circuitry, the high sapphire Q theoretically could make possible long term frequency stability as low as 10.sup.-14 were it not for unwanted temperature fluctuations in the resonator casing. Such a stability would be 20 times better than that achievable by quartz oscillators of the highest quality, which presently provide a stability of 2.times.10.sup.-13.
Various approaches for compensated operation have been developed to reduce thermal variations in electromagnetic or acoustic (piezoelectric) resonators in order to achieve high frequency stability. Compensated operation for bulk acoustic-wave quartz oscillators is achieved by means of an appropriate choice of orientation for the quartz crystal. This is possible due to a very strong variability of acoustic parameters with crystal direction. Electromagnetic sapphire resonators have a much smaller anisotropy (.apprxeq.35%) and no sign reversal for any of its thermal dependencies. In fact, up to the present time useful compensation of sapphire resonators has only been possible at liquid helium temperatures, where incidental or added paramagnetic impurities give an effective compensating effect. But helium temperature operation is expensive, and impractical for most applications. A compensation mechanism for operation at 77.degree. K or above would allow liquid nitrogen to be used as the coolant in a very much smaller Dewar and less expensive compensation mechanism.
Temperature sensitivity of the operating frequency is characteristic of all electromagnetic and acoustic resonators due to thermally induced variation of the size, dielectric constants, speed of sound, etc., for solid state materials. Fractional variation of these parameters is typically 10.sup.4 to 10.sup.5 parts per degree Kelvin. Consequently, achieving resonator stabilities of 10.sup.-13 to 10.sup.-14 would require nanodegree control of temperature stability, an impossible task. Yet such a high degree of stability is desired for use as a stable local oscillator for an atomic frequency standard (atomic clock) of the type disclosed by John D. Prestage in U.S. patent application Ser. No. 08/246,041 titled Extended Linear Ion Trap Frequency Standard Apparatus, now U.S. Pat. No. 5,420,549. The majority of such frequency standards required for various commercial, scientific and military applications are based on quartz crystal oscillators. A sapphire resonator has the potential for greater stability in many such applications.
Available techniques for higher stability and reduced thermal variation in resonator frequencies are:
Very low cryogenic temperatures (T&lt;10.degree. K) can be used to "freeze out" the thermally-induced variations, which vary as a function of T.sup.3 as the temperature of components varies. This technique has been successfully applied to super-conducting, superconductor-on-sapphire, and WG sapphire resonators. However, the very low helium temperature required makes such systems large and expensive, and therefore impractical for most applications. PA1 An inherently weak tuning mechanism may be used at the lowest temperatures to provide complete cancellation. In this way paramagnetic impurities can compensate the thermal variation in sapphire resonators for T.ltoreq.6.degree. K, but again, operation at such low liquid helium temperatures is impractical for most applications. PA1 The differing thermal coefficients for various properties of the resonator components can be played against each other in such a way that, for some operating temperature, thermal frequency variations are compensated or cancelled. Piezoelectric quartz resonators are compensated in this way by an appropriate orientation of this strongly anisotropic crystal (e.g. "SC" or "AT" cut quartz resonators). Unfortunately, an orientation dependent cancellation does not occur for electromagnetic resonators where the anisotropy is much smaller (i.e., where the temperature dependencies vary by only about .apprxeq.30% as the orientation is changed). PA1 A resonator may be constructed using several similar materials with compensating thermal characteristics. For example, dielectric resonators for oscillators are typically stabilized by use of several materials with thermal dielectric variations of opposite sign. PA1 A mechanical tuning mechanism may be driven by thermal expansion coefficients of the construction materials. This mechanism has been previously applied to a sapphire resonator at room temperature using a highly re-entrant geometry to achieve very low phase noise and a stability of 4.times.10.sup.-8 over a period of ten seconds. S. L. Abramov, Ye. N. Ivanov and D. P. Tsarapkin, "A Low-Noise Self-Excited Microwave Oscillator with a Thermally Compensated Disk Dielectric Resonator," Radiotechnika, No. 11, 81-83 (1988), reprinted in English, Telecom & Radio Engineering, Vol. 43, No. 12, pp. 127-129 (1990) and D. P. Tsarapkin, "An Uncooled Microwave Oscillator with 1-Million Effective Q-Factor," Proc. 1993 IEEE International Frequency Control Symposium, pp. 779-783 (1993)!. Ultrahigh frequency stability better than 7.4.times.10.sup.-7 per degree Kelvin was probably precluded by attempting to operate at room temperature with a design using brass and Invar which are alloys having poor thermal conductivity and using two brass parts joined by a sliding (threaded) joint which also has a poor thermal conductivity, thus giving rise to temperature gradients in the compensation mechanism. PA1 Variation of the dielectric constants .epsilon. with temperature is the greatest factor. As shown in FIG. 1, the dielectric constants vary by 80 to 140 parts per million (PPM) per degree Kelvin at room temperature 300.degree. K, as shown by graphs A and B for variations parallel and perpendicular to the resonator axis. The resulting change in frequency f is just half this value, or 40 to 70 PPM per degree Kelvin (since f.varies.1/.sqroot..epsilon.). PA1 The expansion coefficients of sapphire impact the frequency directly giving rise to a frequency change of 5 to 6 PPM per degree Kelvin. PA1 Thermal expansion of a copper rf shielding casing is a small but significant factor. Because microwave energy density at the walls of the casing is greatly reduced (typically 100 to 10,000 times, to enable a high sapphire Q), the frequency sensitivity to casing size is reduced by this same factor. Thus, the 15 PPM per degree Kelvin copper expansion shown in FIG. 2 is reduced to 0.15 PPM per degree Kelvin or less.